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Dependence Properties of B-Spline Copulas

Author

Listed:
  • Xiaoling Dou

    (Waseda University)

  • Satoshi Kuriki

    (The Institute of Statistical Mathematics)

  • Gwo Dong Lin

    (Academia Sinica)

  • Donald Richards

    (Pennsylvania State University)

Abstract

We construct by using B-spline functions a class of copulas that includes the Bernstein copulas arising in Baker’s distributions. The range of correlation of the B-spline copulas is examined, and the Fréchet–Hoeffding upper bound is proved to be attained when the number of B-spline functions goes to infinity. As the B-spline functions are well-known to be an order-complete weak Tchebycheff system from which the property of total positivity of any order follows for the maximum correlation case, the results given here extend classical results for the Bernstein copulas. In addition, we derive in terms of the Stirling numbers of the second kind an explicit formula for the moments of the related B-spline functions on the right half-line.

Suggested Citation

  • Xiaoling Dou & Satoshi Kuriki & Gwo Dong Lin & Donald Richards, 2021. "Dependence Properties of B-Spline Copulas," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 283-311, February.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:1:d:10.1007_s13171-019-00179-y
    DOI: 10.1007/s13171-019-00179-y
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    References listed on IDEAS

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    1. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    2. Shen, Xiaojing & Zhu, Yunmin & Song, Lixin, 2008. "Linear B-spline copulas with applications to nonparametric estimation of copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3806-3819, March.
    3. Huang, J.S. & Dou, Xiaoling & Kuriki, Satoshi & Lin, G.D., 2013. "Dependence structure of bivariate order statistics with applications to Bayramoglu’s distributions," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 201-208.
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